Comments on "The Adjoint Method and Its Application to Trajectory Optimization"

Abstract

A STUDY of the problem of a minimum time transfer between two coplanar circular orbits assuming a constant thrust acceleration has been made, utilizing the Gradient Technique. Optimal steering programs were obtained for values of (thrust acceleration)/(initial gravitational acceleration) from 0.05 to 3.0 and for (radial transfer distance)/(initial orbit rad) values from 0.05 to 1.0. Numerous initial steering programs were used, including those of the form presented by Faulders and by Jurovics and Mclntyre. In all cases, the optimal steering programs obtained were of the form presented by Faulders. Thus the solution presented by Jurovics and Mclntyre appears to be erroneous. For the values of distance ratio (0.5) and acceleration ratio (0.166667) considered by Faulders, a (minimum transfer time)/(time per radian in initial orbit) equal to 3.20608 was obtained. This is substantially in agreement with Faulders' value. For the values of distance ratio (0.1628) and acceleration ratio (1.7343) considered by Jurovics and Mclntyre, a (minimum transfer time)/(time per radian in initial orbit) equal to 0.60946 was obtained. This is a substantial improvement over their solution. The terminal constraint errors for each of the foregoing solutions were less than 3 X 10. ~ Solutions have been obtained using an analog computer as well as the IBM 7090.